Logic and Metaphysics Summary

7/27/2019 Logic and Metaphysics Summary

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Summary of Metaphysics +

Introduction to Logic


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What is Metaphysics

Branch of philosophy concerned with

explaining the fundamental nature of

being and the world


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Causation

Causality (also referred to as causation) is the

relation between an event (the cause) and a

second event (the effect), where the second

event is understood as a consequence of the

first.


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Time

Presentism:

Only the present momentexists, the past andfuture do not.

Eternalism

Future events are"already there", there is

no objective flow of time. The entire universe is

contained within theblock


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Philosophy of mind

Dualism

That the mind and body are two separate

entities.

Monism

That there is only one substance whichcomprises all of existence


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Free will

Hard Determinism

The theory that all human decisions and actions are determined by other events

and actions that happened prior to that moment. This removes any individual

moral responsibility as a persons decisions are determined by external factors.

Libertarianism (Free will)

The theory that we are free to act as we wish and therefore the individual is

morally responsible for their own actions as people are self-determining, whichmeans they make their choices of their own volition.


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Knowledge

Do we possesA Prioriknowledge (knowledge that isacquire BEFORE experience) or onlyA Posterioriknowledge (knowledge that is acquired after someexperience)

I think, therefore I am . Someone S knows that P if and only if:

(1) S believes that P is truei.e. Josh (S) believes that he is Australian (P) (2) P is true

Josh (S) is Australian (P) (3) S isjustified in believing that P is trueJosh is justified in believeing that he is Australian as he hasseen his birth certificate


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What does Judaism say?

Well Judaism contains within an entire metaphysical system

Is it in contradiction with secular philosophy? Depends on the specific philosophy/idea

I certainly think not

Philosophy is, in a sense, a kind of thinking that has a beginningbut no end. In it, the awareness of the problem outlives allsolutions. Its answers are questions in disguise; every new answergiving rise to new questions. In religion, on the other hand, themystery of the answer hovers over all questions. Philosophy deals

with problems as universal issues; to religion the universal issuesare personal problems. Philosophy, then, stresses the primacy ofthe problem, religion stresses the primacy of the person.

Abraham Joshua Heschel


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What we are building towards

Philosophical arguments

Discussions about G-d

This requires us to delve into the world of Logic


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What is Logic

The purpose of logic is to distinguish correct

forms of argument from incorrect forms of

argument

This is done using only the form of the

argument, independently of the subject

matter. What this means is that we can reduce

arguments to symbols and equations.


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Argument

An argument is a statement along with one or

more reasons for thinking that the statement

is true. The reasons or evidence are called the

premises of the argument. The statement the

premises are used to support is called the

conclusion of the argument.


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A good argument

The premises must supportthe conclusion;

the conclusion shouldfollowfrom the

premises.

All the premises must be true.

However there are multiple ways of analyzing

arguments. We are going to cover a few of them

now


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Consistency

A set of sentences is consistent if it is

POSSIBLE for them all to be true.

A set of sentences is inconsistent if it is NOT

POSSIBLE for them all to be true.

POSSIBLE here refers to logical possibility. In

logic the paradigm kind of impossibility is the

CONTRADICTION:


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Example

A is true and A is false

Josh is awesome AND It is not true that Josh is

awesome

Something is logically impossible only if it

entails an outright contradiction like this. i.e. it

is not possible for both of these statements to

be true


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Validity

A valid argument is one in which IF all the

premises are true, the conclusion MUST be

true too. In other words:

A valid argument is one in which it is

IMPOSSIBLE for all the premises to be true

and the conclusion false.

However to be a valid argument it is not

required that the premises be true


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Lets introduce a little bit of Symbology

All P are Q.

All Q are R.

Thus all P are R.

Is this a valid argument?

Yes

Can you see how swapping the letters for any

phrase would still make the argument valid?

Lets see some examples.


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Examples

All Melbournians are Australians.All Australians are Earthlings.

Therefore all Melbournians are Earthlings.

Is this argument valid?

Yes!

All animals live on Mars

All humans are animals

Therefore, all humans live on Mars.


Yes!


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Examples continued

All Melbournians are funny.

All Melbournians are Earthlings.

Therefore all Earthlings are funny.


No

In logic, an argument is valid if and only if its conclusion

is logically entailed by its premises and each step in theargument is logical


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Negation

The negation of a sentence is the sentence

with the opposite truth value.

If the sentence is true, its negation is false and

if the sentence is false, its negation is true.

In Logicians English we can always form the

negation of a sentence by putting the phrase

It is not true that or It is false that in front

of the sentence.


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Sentence Its negation

Josh is Australian It is not true that Josh is Australian

(Josh is not Australian)

All men are pigs It is not true that all men are pigs

(Not all men are pigs or Some men

are not pigs)

Logic is not a useful subject It is not true that logic is not a useful

subject.

(Logic IS a useful subject)


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Consistency and validity



and the conclusion false.

This means that:



and for the NEGATION of the conclusion to be

true.

SO


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SO


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If the premises and the negation of the

conclusion are inconsistent, the argument is

valid.

If the premises and the negation of the

conclusion are consistent, the argument is

invalid.


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Examples

All men are mortal.

Socrates is mortal.

Therefore, Socrates is a man

How about if we swap the conclusion to:

Therefore, it is false that Socrates if a man.

Is this argument consistent?

If the premises and the negation of the conclusionare inconsistent, the argument is valid.


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Examples continued

Here is our example from earlier:

All Melbournians are funny.

All Melbournians are Earthlings.

Therefore all Earthlings are funny.

Lets change our conclusion to it is not true that allEarthlings are funny.

Does the argument still work with this change? Arethe premises and the negation of the conclusionconsistent?


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Validity and soundness

A good argument must satisfy the two

conditions mentioned above. But an argument

can satisfy one condition without satisfying

the other.


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A valid argument can have FALSE premises:

All car manufacturers are computer manufacturers.

Ford is a car manufacturer.

Therefore:

C. Ford is a computer manufacturer.

An argument with TRUE premises might be invalid.Josh is Australian.

Therefore:C. Josh is awesome


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Soundness

An argument which is BOTH valid and has all

true premises is called a SOUND argument.

An argument is sound if and only if

1. The argument is valid.

2. All of its premises are true.


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ExamplesAll organisms with wings can fly.

Penguins have wings.Therefore:

C. Therefore, penguins can fly.

Is this argument sound?

No! All people with the name Josh Back are cool

The Person reading this out has the name Josh Back

Therefore :

C. The person reading this out is cool

Is this argument sound?

Yesthough I guess its a matter of interpretation


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Worksheet

Take a quiz and see if you can work out the

answers. There is one tricky question at the

endlets see if you can solve it

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Logic and Metaphysics Summary